Confinement and center vortices in Coulomb gauge: analytic and numerical results

We review the confinement scenario in Coulomb gauge. We show that when thin center vortex configurations are gauge transformed to Coulomb gauge, they lie on the common boundary of the fundamental modular region and the Gribov region. This unifies elements of the Gribov confinement scenario in Coulomb gauge and the center-vortex confinement scenario. We report on recent numerical studies which support both of these scenarios.Comment: Talk given at QCD Down Under, Adelaide, Australia, March 10-19, 2004. 6 pages. 6 figure

Scaling properties of Wilson loops pierced by P-vortices

P-vortices, in an SU(N) lattice gauge theory, are excitations on the center-projected Z(N) lattice. We study the ratio of expectation values of SU(2) Wilson loops, on the unprojected lattice, linked to a single P-vortex, to that of Wilson loops which are not linked to any P-vortices. When these ratios are plotted versus loop area in physical units, for a range of lattice couplings, it is found that the points fall approximately on a single curve, consistent with scaling. We also find that the ratios are rather insensitive to the point where the minimal area of the loop is pierced by the P-vortex.Comment: 4 pages, 4 figure

Charge Screening, Large-N, and the Abelian Projection Model of Confinement

We point out that the abelian projection theory of quark confinement is in conflict with certain large-N predictions. According to both large-N and lattice strong-coupling arguments, the perimeter law behavior of adjoint Wilson loops at large scales is due to charge-screening, and is suppressed relative to the area term by a factor of $1/N^2$. In the abelian projection theory, however, the perimeter law is due to the fact that $N-1$ out of $N^2-1$ adjoint quark degrees of freedom are (abelian) neutral and unconfined; the suppression factor relative to the area law is thus only $1/N$. We study numerically the behavior of Wilson loops and Polyakov lines with insertions of (abelian) charge projection operators, in maximal abelian gauge. It appears from our data that the forces between abelian charged, and abelian neutral adjoint quarks are not significantly different. We also show via the lattice strong-coupling expansion that, at least at strong couplings, QCD flux tubes attract one another, whereas vortices in type II superconductors repel.Comment: 20 pages (Latex), 8 figures, IFUP-TH 54/9

Remnant Symmetry and the Confinement Phase in Coulomb Gauge

We report on connections between the confining color Coulomb potential, center vortices, and the unbroken realization of remnant gauge symmetry in Coulomb gauge.Comment: 6 pages. Invited talk at "QCD Down Under," Adelaide, Australia, March 200

Dynamical Origin of the Lorentzian Signature of Spacetime

It is suggested that not only the curvature, but also the signature of spacetime is subject to quantum fluctuations. A generalized D-dimensional spacetime metric of the form $g_{\mu \nu}=e^a_\mu \eta_{ab} e^b_\nu$ is introduced, where $\eta_{ab} = diag\{e^{i\theta},1,...,1\}$. The corresponding functional integral for quantized fields then interpolates from a Euclidean path integral in Euclidean space, at $\theta=0$, to a Feynman path integral in Minkowski space, at $\theta=\pi$. Treating the phase $e^{i\theta}$ as just another quantized field, the signature of spacetime is determined dynamically by its expectation value. The complex-valued effective potential $V(\theta)$ for the phase field, induced by massless fields at one-loop, is considered. It is argued that $Re[V(\theta)]$ is minimized and $Im[V(\theta)]$ is stationary, uniquely in D=4 dimensions, at $\theta=\pi$, which suggests a dynamical origin for the Lorentzian signature of spacetime.Comment: 6 pages, LaTe